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Dr Peter Brian Kirkwood (33) and Richard Phillips - who were Christchurch-based engineering geologists – died climbing the mountain on Tuesday.
One of the climbers raised the alarm with police that night, saying the other had fallen.
The bodies were recovered just after 8am today with the help of the Taranaki Rescue Helicopter and police search and rescue and Alpine Cliff Rescue crew.
It followed an unsuccessful attempt to recover the bodies yesterday due to poor conditions.
Kirkwood's wife, Kerrie Ann Kirkwood, today paid tribute to the "skilled and experienced tramper, mountaineer and backcountry skier".
"Kirkwood was born and raised in Cardiff, Wales. The son of Paul and Katrina, brother to Beth, Matthew and Edith," Kerrie Ann Kirkwood said in a statement released to media.
"He met his wife-to-be, Kerrie Ann, in the University of Cambridge Hillwalking Club, while completing a PhD in geotechnical engineering.
"After graduation, they spent time working, skiing and climbing based out of Boulder, Colorado, before moving to New Zealand in 2018.
"The mountains were central to Peter's life. He was a skilled and experienced tramper, mountaineer and backcountry skier, who had climbed numerous peaks in the European Alps, the Scottish Highlands, the North American Rockies, and the New Zealand Southern Alps.
"He had recently become a father, and was looking forward to introducing his baby daughter, Elaine Sierra, to the mountains that he and Kerrie Ann loved so much.
"A competent, careful engineer, who tackled complex geotechnical problems with relish, Peter was held in high esteem by his colleagues at Tonkin & Taylor."
She added: "He was a loyal, considerate and adventurous soul, who will be dearly missed by his friends in the UK, the US, and in Christchurch, where he and Kerrie Ann had made their home.
"Peter's loss leaves a huge hole in the lives of his family and friends. We respectfully request privacy at this difficult time."
A formal identification process will now be undertaken to identify the men, a police statement said earlier.
They were climbing the mountain in their own time.
Tonkin + Taylor managing director Dr Tim Fisher said police told the company yesterday morning that two of their "treasured staff" had been involved in a climbing accident.
"Our priority right now is to support their families and our people as we deal with this incredibly sad news.
"We would like to thank Taranaki police and search and rescue for their service and support," a statement provided to Stuff said.
South Taranaki iwi Ngāruahine posted on Facebook that the men climbed up the summit track from the north but have fallen on the southern side of the summit.
A rāhui is in place on the mountain and will be reviewed a week after the bodies are recovered.
It is understood the accident happened near Syme Hut.
Just two weeks ago Tonkin + Taylor posted a tribute on social media from Phillips for well-respected rope technician Tom Arnold after he died in a rockfall near Lake Manapōuri in Fiordland last month.
He praised Arnold's professionalism and safety-first attitude.